David died at Cedars-Sinai Medical Centre in Los Angeles yesterday of complications from a stroke, his wife Eunice said.
He had suffered a major stroke in March and was stricken again on Tuesday, she said.
"Even at the end, Hal always had a song in his head," she said. "He was always writing notes, or asking me to take a note down, so he wouldn't forget a lyric."
Singer Smokey Robinson praised David's musical legacy. "I hope that the music world will join together in celebrating the life of one of our greatest composers ever," he said.
David and Bacharach won an Oscar for Raindrops Keep Fallin' On My Head from the film Butch Cassidy And The Sundance Kid, Grammys and Tonys for the songs from the hit Broadway musical Promises, Promises, as well as other top 40 hits including Close to You and That's What Friends Are For.
Many of the duo's lyrics and tunes continue to resonate in pop culture, including I Say A Little Prayer, What The World Needs Now Is Love, and This Guy's In Love With You. Their music was recorded by legendary singers including The Beatles, Barbra Streisand, Frank Sinatra, Neil Diamond and their long-time partner Dionne Warwick.
David joined the board of the American Society of Composers, Authors and Publishers in 1974 and was its president from 1980 to 1986. He was head of the Songwriters Hall of Fame from 2001 to 2011, and was Chairman Emeritus at his death.
"As a lyric writer, Hal was simple, concise and poetic - conveying volumes of meaning in fewest possible words and always in service to the music," ASCAP's current president, songwriter Paul Williams, said.
"It is no wonder that so many of his lyrics have become part of our everyday vocabulary and his songs ... the backdrop of our lives."
In May Bacharach and David received the Library of Congress Gershwin Prize for Popular Song during a White House tribute concert attended by President Barack Obama.
Bacharach, 83, thanked Mr Obama, saying the award for his life's work topped even the Oscars and Grammys he won for individual projects. David could not attend but his wife accepted on his behalf.
More than 55 years after their first songs hit the airwaves, Mr Obama said "these guys have still got it". He noted their music was still being recorded by such artists as Alicia Keys and John Legend.
"Above all, they stayed true to themselves," Mr Obama said. "And with an unmistakable authenticity, they captured the emotions of our daily lives - the good times, the bad times, and everything in between."
David and Bacharach met when both worked in the Brill Building, New York's legendary Tin Pan Alley song factory where writers cranked out songs and attempted to sell them to music publishers. They scored their first big hit with Magic Moments, a million-selling record for Perry Como.
In 1962, they began writing for a young singer named Dionne Warwick, whose versatile voice conveyed the emotion of David's lyrics and easily handled the changing patterns of Bacharach's melodies. Together the trio created a succession of popular songs including Don't Make Me Over, Walk On By, I Say a Little Prayer, Do You Know The Way To San Jose, Trains And Boats And Planes, Anyone Who Had A Heart, You'll Never Get To Heaven and Always Something There To Remind Me.
The pair also wrote hit songs for numerous other singers: This Guy's In Love with You (trumpeter Herb Alpert in his vocal debut); Make It Easy On Yourself (Jerry Butler); What The World Needs Now is Love (Jackie DeShannon); and Wishin' And Hopin' (Dusty Springfield).
They also turned out title songs for the movies What's New, Pussycat (Tom Jones) and Wives And Lovers (Jack Jones).
In a 1999 interview, David explained his success as a lyricist this way: "Try and tell a narrative. The songs should be like a little film, told in three or four minutes. Try to say things as simply as possible, which is probably the most difficult thing to do."
The writer, who lived in New York, often flew to Los Angeles, where he and Bacharach would hole up for a few weeks of intense songwriting. Sometimes they conferred by long-distance telephone; I Say A Little Prayer was written that way.
The hit-making team broke up after the 1973 musical remake of Lost Horizon. They had devoted two years to the movie, only to see it scorned by critics and audiences alike. Bacharach became so depressed he isolated himself in his holiday home and refused to work.
Bacharach and David sued each other and Warwick sued them both. The cases were settled out of court in 1979 and the three went their separate ways. They reconciled in 1992 for Warwick's recording of Sunny Weather Lover.
David, meanwhile, went on to collaborate successfully with several other composers: John Barry with the title song of the James Bond film Moonraker; Albert Hammond with To All The Girls I've Loved Before, on which Julio Iglesias and Willie Nelson dueted; and Henry Mancini with The Greatest Gift in The Return Of The Pink Panther.
Born in New York City, David had attended state schools before studying journalism at New York University.
He served in the army during the Second World War, mostly as a member of an entertainment unit in the South Pacific.
After the war, he wrote lyrics for several composers until that fateful Brill Building meeting with Bacharach.
David was married to Eunice for 25 years. He had two sons, Jim and Craig, from a previous marriage to Anne Rauchman.
A private memorial service is planned.
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